 Linearization error in synchronization of Kuramoto oscillatorsSamira Hossein Ghorban, Fatemeh Baharifard, Bardyaa Hesaam, Mina Zarei and Hamid Sarbazi-Azad Applied Mathematics and Computation, 2021, vol. 411, issue C Abstract: Synchronization among a set of networked nodes has attracted much attention in different fields. This paper thoroughly investigates linear formulation of the Kuramoto model, with and without frustration, for an arbitrarily weighted undirected network where all nodes may have different intrinsic frequencies. We develop a mathematical framework to estimate errors of the linear approximation for globally and locally coupled networks. We mathematically prove that the eigenvector corresponding to the largest eigenvalue of the network’s Laplacian matrix is enough for examining synchrony alignment and that the functionality of this vector depends on the corresponding eigenvalue. Moreover, we prove that if a globally coupled network with frustration has perfect phase synchronization when its coupling strength tends to infinity, it is a regular network. Finally, the effect of correlation between frustration values and degrees (or frequencies) on the synchronizability of the network is investigated. Keywords: Networks; Social networks; Synchronization; Kuramoto model; Linearization; Error estimation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321005531 DOI: 10.1016/j.amc.2021.126464 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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